converted the former Lagrange multiplier into a canonical propagating field. It also made the coupling between \(T\)  and \(X\)  proportional to \( {1\over \sqrt{Z_T} }\) . This feature of the coupling is the reason for the problem: The model in [1]} encounters a singularity on the way back to \(Z_T=0\) . If this singularity would be only in the sector of scalar fields with positive mass squared, it might work well towards the limit to the original VA fermionic theory as these heavy scalars would decouple from the spectrum. But such a singularity in the tachyonic sector of the theory shows that the theory is not related to a fermionic model since there is an instant vacuum instability with respect to the generation of classical scalar fields, instead of decoupling.
